Newton’s Second Law of
Motion
Force and Acceleration
Movement

When we see something move we see
Start
 Slow
 Curve
 Stop


All these things represent a CHANGE in
motion
Formulas to remember

Acceleration = change in velocity
time interval

What is the cause of acceleration?

FORCE
Force causes Acceleration

Example – hockey puck in ice
Still until force is placed on it
 Stays moving in a straight path until another
force causes it to accelerate

Change direction
 Speed up
 Slow down


Change in velocity  acceleration
Net force causes acceleration
Combination of force yields acceleration
 Double the force – double the
acceleration
 Mathematically –

Acceleration ~ net force
 “~” means “directly proportional to”

Mass resists acceleration

Example
Full shopping cart vs. empty shopping cart
 The greater the mass the more force it
takes to accelerate the object


Acceleration is inversely proportional to
mass

Acceleration ~
1
mass
As the denominator
increased the whole
quantity decreases
Newton’s Second Law
The acceleration produced by the force
on an object is directly proportional to the
magnitude of the net force, is in the
same direction as the net force and is
inversely proportional to the mass of the
object
 Mathematically:
acceleration~ net force
mass

Applications of 2nd Law
Using consistent units
a=F
m
 a =acceleration
(m/sec^2 )
 F = force
(newtons)
 m = mass (kg)

Acceleration – which way?
Net force action on an object
and its resulting acceleration
are always in the same
direction
 The spool demo:

Which way will it roll?
 Does it change from top to
bottom?

Problem Solving

One Newton – the force
needed to give a mass of one
kilogram an acceleration of
one meter per second per
second.
1 N = (1 kg) (1 m/sec/sec)
 1 N = 1 kg m/ sec^2
 If we know two quantities, we can
solve for the third

Problem 1

How much force, or thrust, must a
30,000-kg jet plane develop to achieve
an acceleration of 1.5 m/sec^2

F = ma
= (30,000 kg)(1.5 m/sec^2)
= 45,000 kg m/sec^2
= 45,000 N
Problem 2
What acceleration is produced by a force
of 2000 N applied to a 1000-kg car?
 a = F/m
= 2000 N/ 1000 kg
= 2000 kg m/sec^2/1000 kg
= 2 m/sec^2


If the force is 4000 N, the acceleration doubles
 4000N/1000 kg = 4 m/sec^2
Questions
If a car accelerates at 2 m/sec^2, what
acceleration can it attain if it is towing
another car of equal mass?
 Answer – the same force on twice the
mass produces half the acceleration or
1 m/sec^2

Questions
What kind of motion does a constant
force produce on an object of fixed
mass?
 A constant force produces motion at a
constant acceleration, in accordance
with Newton’s second law.

Friction
Is a force
 Must be in contact
 Direction opposite
to motion
 Force is needed to
overcome friction
 Caused by
irregular surface

Extent of friction
Depends on kinds of
material
 How much surface are
pressed together
 Examples

Rubber on concrete
 Steel on steel
 Guard rails are now
concrete instead of steel

Friction in Fluids
Fluids – liquids and gases
 Caused by object trying to move
particles apart in order to pass
thru it


Try to run in water?

Liquid friction can be quite high
 Air resistance – notice at high
speeds

Biking or skiing
Friction and Force
When friction is present, object may only
move at a constant speed even if you
apply force (instead of accelerating)
 The net force is zero

Air Resistance
PUSH
Weight
FRICTION
Questions
Two forces act on a book resting on a
table: its weight and the support force
from the table. Does a force of friction
act as well?
 No, not unless the book tends to slide.
Friction only acts when there is motion

Question

Suppose a high-flying jet cruises with a
constant velocity when the thrust from its
engines is a constant 80,000 N. What is
the acceleration of the jet? What is the
force of air resistance acting on the jet?
Answer

The acceleration must be zero because
the velocity is constant. Since the
acceleration is zero, if follows a = F/m
the net force is zero. This means the
force of air resistance is 80,000 N and it
acts in the direction opposite to the jet’s
motion.
Applying Force - Pressure

No matter how you place a book on
a table, the force is the same


Try varying the way it is placed on a
scale
However – place a book on your
palm or on top of a pencil which
goes into your hand……

PRESSURE – has to do with force and
area
Pressure
The amount of force per unit area
 Pressure = force
area of application
P=F
A
P=pressure (pascals)
F= force (newtons)
A = area (meter^2)


1 Pascal = 1 N/m^2
Pressure comparisons

Pressure on your foot
Two feet
 One foot
 Pointe (ballerina)


Calculating the pressure on your foot
with graph paper
Bed of Nails Questions
In attempting to do a
bed of nails, would it be
wise to begin with a few
nails and work upward
to more nails?
 No, no, no! There
would be less physics
teachers with fewer
nails. The resulting
greater pressure would
cause harm.

Bed of Nails question

The massiveness of the cement block plays an
important role in this demo. Which provides
more safety, a small block or a more massive
block?
 The greater the mass, the smaller the
acceleration of the block and the bed of nails
towards the friend. Much of the force from the
hammer goes into breaking the block. The
block must be BIG and must BREAK!
Free Fall explained

Galileo did his famous
experiment off the leaning
tower of Pisa.
Dropped a 10 kg cannon
ball
 Dropped a 1 kg stone at
same time
 Result – accelerations are
equal


But why?
Newton’s law
F = ma
 Therefore a = F/m

If an item is large it has a large force and a
large mass
 If an item is small, it has a small force and a
small mass
 Either way the RATIOS are the same


F/m
= F/m
Galileo's experiment
a = F/m = 9.8 N/ 1 kg rock = 9.8 m/sec^2
 a = F/m = 98 N/10 kg cannon ball= 9.8 m/sec^2


Question – if you were on the moon an
dropped a hammer and a feather at the
same time, would they strike the surface
of the moon at the same time?
Answer

Yes. Astronaut
David Scott did this
exact experiment on
the moon. They
both accelerated at
1/6 g.
Falling and Air resistance

Example – feather and coin in a tube.
With air – coin falls rapidly, the feather
flutters down
 Without air – both reach the bottom at the
same time

Air resistance
feather
coin
weight
Terminal Speed or Velocity

Speed during freefall, when the air
resistance on the object equals the
weight of the falling object.

Terminal speeds of various objects
Feather – 5 m/sec
 Coin – 200 km/hr
 Skydiver – 150 – 200 km/h
 Parachute – 15-25 km/h

Question

If a heavy person and a light person
open their parachutes together at
the same altitude and each wears
the same size parachute, who will
reach the ground first?
 The heavy person. Light person
reaches terminal speed first and it
will be slower than terminal speed
for the heavy person.